1. Field of the Invention
The present invention is directed to a sine-wave oscillator which produces a sine-wave in successive steps, each step consisting of only one multiplication and one addition.
2. Description of the Prior Art
A sine-wave oscillator which produces a sine-wave in successive steps, each step consisting of only one multiplication and one addition is known (Wireless World, June 1981, pp. 69, 70, 78, and wireless World, Nov. 1982, p. 65). Starting from the addition therefrom of the sine, i.e., EQU sin(.omega.+.DELTA..omega.)=sin.omega. cos.DELTA..omega.+cos.omega..multidot.sin.omega..DELTA.,
or the general relationship derived therefrom when considering a discrete point of the sine function, i.e., EQU A.sub.(i+1) =A.sub.i .multidot.cos z+B.sub.i .multidot.sin z,
wherein A.sub.i and B.sub.i are the respective previous sine or cosine values, and A.sub.(i+1) is the newly calculated sine value, and z is a factor proportional to the desired frequency f, this known sine-wave oscillator is based on the realization that for small z, cos z=1 and sin z=z. With this simplification, the above relationship is reduced to EQU A.sub.(i+1) =A.sub.i +B.sub.i .multidot.z.
From this approximate formula it is apparent that a new sine value is respectively obtained by addition of a fraction of the cosine, and in the same way a new cosine can be obtained by subtraction of a fraction of the sine. By this approximation formula the known sine-wave oscillator calculates sequentially, by means of only one multiplication step and one addition step, a new sine value A.sub.(i+1) and cosine value B.sub.(i+1) from the previous sine value A.sub.i and cosine value B.sub.i, respectively, z being a fraction of the radian frequency of the desired frequency value f. The approximation formulae on which the known sine-wave oscillator is based are then, however, mathematically no longer accurate, and therefore the sine-wave signals produced by the known oscillator exhibit fundamental errors with respect to both amplitude and frequency.